Final answer:
The algebraic equation is simplified and solved by expanding, rearranging terms, and factoring to find w, with the solutions being w = -3 or w = 2.
Step-by-step explanation:
The given equation (w+7)² = 2w² + 15w + 43 is an algebraic equation that requires simplification and solving for w. To solve this, we start by expanding the left side of the equation: (w+7)(w+7) = w² + 14w + 49. Then, we set the equation equal to zero by bringing all terms to one side: 0 = 2w² + 15w + 43 - (w² + 14w + 49). Simplifying this gives us w² + w - 6 = 0, which is a quadratic equation that can be solved for w using the quadratic formula or by factoring. Through factoring, we find that (w+3)(w-2) = 0, giving us two possible solutions for w: w = -3 or w = 2.